Inadmissibility of the corrected Akaike information criterion

Abstract: For the multivariate linear regression model with unknown covariance, the corrected Akaike information criterion is the minimum variance unbiased estimator of the expected Kullback--Leibler discrepancy. In this study, based on the loss estimation framework, we show its inadmissibility as an estimator of the Kullback--Leibler discrepancy itself, instead of the expected Kullback--Leibler discrepancy. We provide improved estimators of the Kullback--Leibler discrepancy that work well in reduced-rank situations and examine their performance numerically.